(2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.5

Size: px
Start display at page:

Download "(2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.5"

Transcription

1 2007/5/14 II II x i x i 1 x i x i x i x x+dx f(x)dx f(x) f(x) + 0 f ( x) dx = 1 (Probability Density Funtion 2 ) (normal distribution) ( x m) / 2σ f ( x) = e 2πσ x m 2 N(m, 2 ) N(0,1) 1 2 PDF Adobe PDF 3 1

2 (2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.50, 1. 00, 2.00, N(0,1) , , , , normdist1.f FUNCTION =========================== Funtion NRMDST =========================== real*8 funtion nrmdst(x, m, v) =========================== Delaration of Arguments impliit none real*8 x, m, v =========================== Constants real*8 PI parameter (PI= d0) =========================== Funtion nrmdst = dexp (-(x - m)**2.0d0 / 2.0d0 / v) $ / $ dsqrt(2.0d0 * PI * v) end FUNCTION SUBROUTINE impliit none d0 REAL*8 56 PARAMETER PARAMETER( = ) x 5 REAL*8 FUNCTION SUBROUTINE 6 dble dble( ) 7 PARAMETER PARMATER(xdim=9, ydim=8, xydim=xdim*ydim) 8 DIMENSION PARAMETER C #define 2

3 SUBROUTINE. 11 Subroutine subroutine radiat $ ( I sun, solar, I dust, o2, O langwv, shrtwv $ ) I SUBROUTINE INPUT O SUBROUTINE FORTRAN v 2 dsqrt(2.0d0 * PI * v) (dsqrt(2.0d0 * PI) * dsqrt(v)) dsqrt dsqrt(2.0d0*pi) PARAMETER PI2SQR (PI2SQR * dsqrt(v)) 9 FORTRAN

4 (2-2) x N(0,1) f(x) REAL*8 FUNCTION STDNRM(x) ( x REAL*8 ) FUNCTION NRMDST impliit none real*8 x real*8 nrmdst stdnrm = nrmdst(x, 0.0d0, 1.0d0) ========================= x i x x a ( a x i a) x x a ( a x a) % a F(t) 12 F ( t) = f ( x) dx f(x) x 13 df( x) F(x) 0 0 lim F( x) = 0 lim F( x) = 1 dx x x m F(m+x)+F(m-x)=1, F(m)=0.5 (2-1) [a]n(0,1) 0.01 f(x) 0.00 x 4.00 x 0.01 F(x) erf1.txt PROGRAM ERF1( erf1.f) STDNRM 12 F(x) F(t) F(x) 13 y=f(x), y=x 4

5 program ERF1 Variables impliit none real*8 stdnrm real*8 x, minx, maxx, step real*8 nd, sum, prev integer i, ifirst, ilast Constants parameter (maxx=4.0d0, minx=0.01d0, step=0.01d0) Main Open File open(1, FILE='erf1.txt') Initialize ifirst = int(minx / step) ilast = int(maxx / step) sum = 0.5 prev = stdnrm(0.0d0) write first value (for x=0.0) write(6,1000)0.0, sum write(1,1000)0.0, sum Loop do i = ifirst, ilast x = dble(i) * step nd = stdnrm(x) sum = sum + $ ( step * ( nd + prev ) / 2 ) write(6, 1000)x, sum write(1, 1000)x, sum nd (f(x) ) --> prev prev = nd end do 1000 format(f6.2, F12.8) File Close lose(1) stop end 5

6 x (maxx, minx) (step) PARAMETER i maxx, minx, step f(x) f(x- x) f(x) prev FORMAT WRITE (2-3) erf1.txt N(0,1) F(1.0), F(2.0), F(3.0) F(x)=0.995 F(x)=0.975 x 14 ========= (2-4a) erf1.f erf2.f x<0-4 x 4 x 0.01 f(x), F(x) NDST, ERFA( ERFA(1)=F(0.01), ERFA(2)=F(0.02) ) x F(x) 2-1 nd-and-erf.dat (2-4b) N(0,1) f(x) F(x) 14 F(x)

7 erf2.f Initialize ifirst = int(minx / step) ilast = int(maxx / step) sum = 0.5 prev = stdnrm(0.0d0) Loop (for x>0) do i = ifirst, ilast x = dble(i) * step nd = stdnrm(x) sum = sum + $ ( step * ( nd + prev ) / 2 ) Store (tentative) results into arrays ndist(i) = nd erfa(i) = sum nd (f(x) ) --> prev prev = nd end do Calulation Finished Writing... Open File open(1, FILE='nd-and-erf.dat') (x:negative value) do i=ilast, ifirst, -1 x = - step * dble(i) write(6,1000)x, ndist(i), 1.0d0 - erfa(i) write(1,1000)x, ndist(i), 1.0d0 - erfa(i) end do (x:zero) x = 0.0d0 nd = stdnrm(x) write(6,1000)x, nd, 0.5 write(1,1000)x, nd, 0.5 (x:positive value) do i=ifirst, ilast x = step * dble(i) write(6,1000)x, ndist(i), erfa(i) write(1,1000)x, ndist(i), erfa(i) end do 1000 format(f6.2, 2F12.8) File Close lose(1) 7

8 F(x) x Hastings Hasting x 0 N(0,1) F(x) 1-0.5/w w=(a 0 + a x 1 + a 2 x 2 + a 3 x 3 + a 4 x 4 ) 4 a 0 =1.0, a 1 = , a 2 = , a 3 = , a 4 = x<0 F(x)=1-F( x ) 2-2 Hastings N(0,1) F(x) x FUNCTION ERFH4(x) ========================================================= Funtion ERFH4 N(0,1) F(x) Hastings 4 real*8 funtion erfh4(x) Delaration of Arguments and Funtions impliit none real*8 x, x1 real*8 w real*8 a0, a1, a2, a3, a4 parameter (a0 = 1.0, a1 = , $ a2 = , a3 = , a4 = ) Funtion x1 = dabs(x) w = a0 + a1 * x1 + a2 * x1 ** 2 + a3 * x1 ** 3 + a4 * x1 ** 4 w = w ** 4.0 if x >= 0 then erfh4 = / w else erfh4 = 0.5 / w end if end sign if ========================================================= Funtion ERFH4 N(0,1) F(x) Hastings 4 8

9 real*8 funtion erfh4(x) Delaration of Arguments and Funtions impliit none real*8 x real*8 w real*8 a0, a1, a2, a3, a4 parameter (a0 = 1.0, a1 = , $ a2 = , a3 = , a4 = ) Funtion w = a0 + x * (a1 + x * (a2 + x * (a3 + x * a4))) w = w ** 4.0 sign x erfh4 = sign( / w, x) end (2-5) 2.4 FUNCTION erfh4 x=-4.00,-3.99,,3.99,4.00 x, f(x), 2.4 F(x) Hastings F(x) nd-and-erf-hastings4.dat F(x) 9

10 2. X,Y Satter Diagram x (A vs B : r ) (A vs C : r (A vs D : r ) y i AvsB AvsC y i y i y i x i i y i y=ax+b x i y i y i y i y i (y i y i )=0 ( ) (y i y i ) 2 ( ) (y i y i ) 2 (ax i +by i y i ) 2 a b a b 0 a a = x y n x y ( x x)(y y) i i i i = 2 2 ) 2 x n x ( xi x i b y y = a( x x) x,y 10

11 2-6 INTEGER N,REAL*8 X(1000),Y(1000) R, A B SUBROUTINE REGRES N,X,Y,R,A,B orr.txt A B A B A D regres1.f 3. log y x x,y 11

12 15 proxy data 2-7 arib.dat orr.f A4 PDF DOC

Microsoft Word - 03-数値計算の基礎.docx

Microsoft Word - 03-数値計算の基礎.docx δx f x 0 + δ x n=0 a n = f ( n) ( x 0 ) n δx n f x x=0 sin x = x x3 3 + x5 5 x7 7 +... x ( ) = a n δ x n ( ) = sin x ak = (-mod(k,2))**(k/2) / fact_k 10 11 I = f x dx a ΔS = f ( x)h I = f a h I = h b (

More information

Microsoft Word - 資料 (テイラー級数と数値積分).docx

Microsoft Word - 資料 (テイラー級数と数値積分).docx δx δx n x=0 sin x = x x3 3 + x5 5 x7 7 +... x ak = (-mod(k,2))**(k/2) / fact_k ( ) = a n δ x n f x 0 + δ x a n = f ( n) ( x 0 ) n f ( x) = sin x n=0 58 I = b a ( ) f x dx ΔS = f ( x)h I = f a h h I = h

More information

1. A0 A B A0 A : A1,...,A5 B : B1,...,B

1. A0 A B A0 A : A1,...,A5 B : B1,...,B 1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)

More information

演習2

演習2 神戸市立工業高等専門学校電気工学科 / 電子工学科専門科目 数値解析 2017.6.2 演習 2 山浦剛 (tyamaura@riken.jp) 講義資料ページ h t t p://clim ate.aic s. riken. jp/m embers/yamaura/num erical_analysis. html 曲線の推定 N 次多項式ラグランジュ補間 y = p N x = σ N x x

More information

y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4

y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4 Simpson H4 BioS. Simpson 3 3 0 x. β α (β α)3 (x α)(x β)dx = () * * x * * ɛ δ y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f()

More information

joho09.ppt

joho09.ppt s M B e E s: (+ or -) M: B: (=2) e: E: ax 2 + bx + c = 0 y = ax 2 + bx + c x a, b y +/- [a, b] a, b y (a+b) / 2 1-2 1-3 x 1 A a, b y 1. 2. a, b 3. for Loop (b-a)/ 4. y=a*x*x + b*x + c 5. y==0.0 y (y2)

More information

. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u(

. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u( 3 8. (.8.)............................................................................................3.............................................4 Nermark β..........................................

More information

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 1 21 10 5 1 E-mail: qliu@res.otaru-uc.ac.jp 1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 B 1.1.3 boy W ID 1 2 3 DI DII DIII OL OL 1.1.4 2 1.1.5 1.1.6 1.1.7 1.1.8 1.2 1.2.1 1. 2. 3 1.2.2

More information

Fortran90/95 [9]! (1 ) " " 5 "Hello!"! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1

Fortran90/95 [9]! (1 )   5 Hello!! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1 Fortran90/95 2.1 Fortran 2-1 Hello! 1 program example2_01! end program 2! first test program ( ) 3 implicit none! 4 5 write(*,*) "Hello!"! write Hello! 6 7 stop! 8 end program example2_01 1 program 1!

More information

(Basic Theory of Information Processing) Fortran Fortan Fortan Fortan 1

(Basic Theory of Information Processing) Fortran Fortan Fortan Fortan 1 (Basic Theory of Information Processing) Fortran Fortan Fortan Fortan 1 17 Fortran Formular Tranlator Lapack Fortran FORTRAN, FORTRAN66, FORTRAN77, FORTRAN90, FORTRAN95 17.1 A Z ( ) 0 9, _, =, +, -, *,

More information

11042 計算機言語7回目 サポートページ:

11042 計算機言語7回目  サポートページ: 11042 7 :https://goo.gl/678wgm November 27, 2017 10/2 1(print, ) 10/16 2(2, ) 10/23 (3 ) 10/31( ),11/6 (4 ) 11/13,, 1 (5 6 ) 11/20,, 2 (5 6 ) 11/27 (7 12/4 (9 ) 12/11 1 (10 ) 12/18 2 (10 ) 12/25 3 (11

More information

コンピュータ概論

コンピュータ概論 4.1 For Check Point 1. For 2. 4.1.1 For (For) For = To Step (Next) 4.1.1 Next 4.1.1 4.1.2 1 i 10 For Next Cells(i,1) Cells(1, 1) Cells(2, 1) Cells(10, 1) 4.1.2 50 1. 2 1 10 3. 0 360 10 sin() 4.1.2 For

More information

all.dvi

all.dvi fortran 1996 4 18 2007 6 11 2012 11 12 1 3 1.1..................................... 3 1.2.............................. 3 2 fortran I 5 2.1 write................................ 5 2.2.................................

More information

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C 8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,

More information

ii

ii ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................

More information

1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 5 3. 4. 5. A0 (1) A, B A B f K K A ϕ 1, ϕ 2 f ϕ 1 = f ϕ 2 ϕ 1 = ϕ 2 (2) N A 1, A 2, A 3,... N A n X N n X N, A n N n=1 1 A1 d (d 2) A (, k A k = O), A O. f

More information

9 8 7 (x-1.0)*(x-1.0) *(x-1.0) (a) f(a) (b) f(a) Figure 1: f(a) a =1.0 (1) a 1.0 f(1.0)

9 8 7 (x-1.0)*(x-1.0) *(x-1.0) (a) f(a) (b) f(a) Figure 1: f(a) a =1.0 (1) a 1.0 f(1.0) E-mail: takio-kurita@aist.go.jp 1 ( ) CPU ( ) 2 1. a f(a) =(a 1.0) 2 (1) a ( ) 1(a) f(a) a (1) a f(a) a =2(a 1.0) (2) 2 0 a f(a) a =2(a 1.0) = 0 (3) 1 9 8 7 (x-1.0)*(x-1.0) 6 4 2.0*(x-1.0) 6 2 5 4 0 3-2

More information

³ÎΨÏÀ

³ÎΨÏÀ 2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p

More information

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,. 24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)

More information

1 u t = au (finite difference) u t = au Von Neumann

1 u t = au (finite difference) u t = au Von Neumann 1 u t = au 3 1.1 (finite difference)............................. 3 1.2 u t = au.................................. 3 1.3 Von Neumann............... 5 1.4 Von Neumann............... 6 1.5............................

More information

untitled

untitled Fortran90 ( ) 17 12 29 1 Fortran90 Fortran90 FORTRAN77 Fortran90 1 Fortran90 module 1.1 Windows Windows UNIX Cygwin (http://www.cygwin.com) C\: Install Cygwin f77 emacs latex ps2eps dvips Fortran90 Intel

More information

Collatzの問題 (数学/数理科学セレクト1)

Collatzの問題 (数学/数理科学セレクト1) / AICHI UNIVERSITY OF EDUCATION A { z = x + iy 0.100

More information

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

120802_MPI.ppt

120802_MPI.ppt CPU CPU CPU CPU CPU SMP Symmetric MultiProcessing CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CP OpenMP MPI MPI CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU MPI MPI+OpenMP CPU CPU CPU CPU CPU CPU CPU CP

More information

Microsoft Word - 資料 docx

Microsoft Word - 資料 docx y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 29 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 30 L A x y A L x 31 plot sine curve program sine implicit

More information

1. A0 A B A0 A : A1,...,A5 B : B1,...,B

1. A0 A B A0 A : A1,...,A5 B : B1,...,B 1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A, B Z Z m, n Z m n m, n A m, n B m=n (1) A, B (2) A B = A B = Z/ π : Z Z/ (3) A B Z/ (4) Z/ A, B (5) f : Z Z f(n) = n f = g π g : Z/ Z A, B (6)

More information

tokei01.dvi

tokei01.dvi 2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN

More information

Microsoft Word - 触ってみよう、Maximaに2.doc

Microsoft Word - 触ってみよう、Maximaに2.doc i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x

More information

01_OpenMP_osx.indd

01_OpenMP_osx.indd OpenMP* / 1 1... 2 2... 3 3... 5 4... 7 5... 9 5.1... 9 5.2 OpenMP* API... 13 6... 17 7... 19 / 4 1 2 C/C++ OpenMP* 3 Fortran OpenMP* 4 PC 1 1 9.0 Linux* Windows* Xeon Itanium OS 1 2 2 WEB OS OS OS 1 OS

More information

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j ) 5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y

More information

情報処理概論(第二日目)

情報処理概論(第二日目) 情報処理概論 工学部物質科学工学科応用化学コース機能物質化学クラス 第 8 回 2005 年 6 月 9 日 前回の演習の解答例 多項式の計算 ( 前半 ): program poly implicit none integer, parameter :: number = 5 real(8), dimension(0:number) :: a real(8) :: x, total integer

More information

25 II :30 16:00 (1),. Do not open this problem booklet until the start of the examination is announced. (2) 3.. Answer the following 3 proble

25 II :30 16:00 (1),. Do not open this problem booklet until the start of the examination is announced. (2) 3.. Answer the following 3 proble 25 II 25 2 6 13:30 16:00 (1),. Do not open this problem boolet until the start of the examination is announced. (2) 3.. Answer the following 3 problems. Use the designated answer sheet for each problem.

More information

3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t + u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,., ν. t +

3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t + u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,., ν. t + B: 2016 12 2, 9, 16, 2017 1 6 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : t = ν 2 u x 2, (1), c. t + c x = 0, (2). e-mail: iwayama@kobe-u.ac.jp,. 1 3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t +

More information

, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x

, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x 1 1.1 4n 2 x, x 1 2n f n (x) = 4n 2 ( 1 x), 1 x 1 n 2n n, 1 x n n 1 1 f n (x)dx = 1, n = 1, 2,.. 1 lim 1 lim 1 f n (x)dx = 1 lim f n(x) = ( lim f n (x))dx = f n (x)dx 1 ( lim f n (x))dx d dx ( lim f d

More information

A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P

A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P 1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A

More information

08 p Boltzmann I P ( ) principle of equal probability P ( ) g ( )g ( 0 ) (4 89) (4 88) eq II 0 g ( 0 ) 0 eq Taylor eq (4 90) g P ( ) g ( ) g ( 0

08 p Boltzmann I P ( ) principle of equal probability P ( ) g ( )g ( 0 ) (4 89) (4 88) eq II 0 g ( 0 ) 0 eq Taylor eq (4 90) g P ( ) g ( ) g ( 0 08 p. 8 4 k B log g() S() k B : Boltzmann T T S k B g g heat bath, thermal reservoir... 4. I II II System I System II II I I 0 + 0 const. (4 85) g( 0 ) g ( )g ( ) g ( )g ( 0 ) (4 86) g ( )g ( 0 ) 0 (4

More information

num3.dvi

num3.dvi kanenko@mbk.nifty.com http://kanenko.a.la9.jp/ ,, ( ) Taylor. ( 1) i )x 2i+1 sinx = (2i+1)! i=0 S=0.0D0 T=X; /* */ DO 100 I=1,N S=S+T /* */ T=-T*X*X/(I+I+2)/(I+I+3) /* */ 100 CONTINUE. S=S+(-1)**I*X**(2*i+1)/KAIJO(2*I+1).

More information

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,. (1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..

More information

3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,.,

3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,., B:,, 2017 12 1, 8, 15, 22 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : u t = ν 2 u x 2, (1), c. u t + c u x = 0, (2), ( ). 1 3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2,

More information

Evoltion of onentration by Eler method (Dirihlet) Evoltion of onentration by Eler method (Nemann).2 t n =.4n.2 t n =.4n : t n

Evoltion of onentration by Eler method (Dirihlet) Evoltion of onentration by Eler method (Nemann).2 t n =.4n.2 t n =.4n : t n 5 t = = (, y, z) t (, y, z, t) t = κ (68) κ [, ] (, ) = ( ) A ( /2)2 ep, A =., t =.. (69) 4πκt 4κt = /2 (, t) = for ( =, ) (Dirihlet ondition) (7) = for ( =, ) (Nemann ondition) (7) (68) (, t) = ( ) (

More information

フローチャートの書き方

フローチャートの書き方 アルゴリズム ( 算法 ) 入門 1 プログラムの作成 機械工学専攻泉聡志 http://masudahp.web.fc2.com/flowchart/index.html 参照 1 何をどのように処理させたいのか どのようなデータを入力し どのような結果を出力させるのか問題を明確にする 2 問題の内容どおりに処理させるための手順を考える ( フローチャートの作成 )~アルゴリズム( 算法 ) の作成

More information

main.dvi

main.dvi 1 F77 5 hmogi-2008f@kiban.civil.saitama-u.ac.jp 2013/5/13 1 2 f77... f77.exe f77.exe CDROM (CDROM D D: setupond E E: setupone 5 C:work\T66160\20130422>f77 menseki.f -o menseki f77(.exe) f77 f77(.exe) C:work\T66160\20130422>set

More information

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) Carathéodory 10.3 Fubini 1 Introduction 1 (1) (2) {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) Carathéodory 10.3 Fubini 1 Introduction 1 (1) (2) {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a % 100% 1 Introduction 2 (100%) 2.1 2.2 2.3 3 (100%) 3.1 3.2 σ- 4 (100%) 4.1 4.2 5 (100%) 5.1 5.2 5.3 6 (100%) 7 (40%) 8 Fubini (90%) 2007.11.5 1 8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory

More information

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë 2012 5 24 scalar Open MP Hello World Do (omp do) (omp workshare) (shared, private) π (reduction) PU PU PU 2 16 OpenMP FORTRAN/C/C++ MPI OpenMP 1997 FORTRAN Ver. 1.0 API 1998 C/C++ Ver. 1.0 API 2000 FORTRAN

More information

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9 1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),

More information

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë 2011 5 26 scalar Open MP Hello World Do (omp do) (omp workshare) (shared, private) π (reduction) scalar magny-cours, 48 scalar scalar 1 % scp. ssh / authorized keys 133. 30. 112. 246 2 48 % ssh 133.30.112.246

More information

- II

- II - II- - -.................................................................................................... 3.3.............................................. 4 6...........................................

More information

インテル(R) Visual Fortran Composer XE 2013 Windows版 入門ガイド

インテル(R) Visual Fortran Composer XE 2013 Windows版 入門ガイド Visual Fortran Composer XE 2013 Windows* エクセルソフト株式会社 www.xlsoft.com Rev. 1.1 (2012/12/10) Copyright 1998-2013 XLsoft Corporation. All Rights Reserved. 1 / 53 ... 3... 4... 4... 5 Visual Studio... 9...

More information

r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B

r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B 1 1.1 1 r 1 m A r/m i) t ii) m i) t Bt; m) Bt; m) = A 1 + r ) mt m ii) Bt; m) Bt; m) = A 1 + r ) mt m { = A 1 + r ) m } rt r m n = m r m n Bt; m) Aert e lim 1 + 1 n 1.1) n!1 n) e a 1, a 2, a 3,... {a n

More information

Fortran90/95 2. (p 74) f g h x y z f x h x = f x + g x h y = f y + g y h z = f z + g z f x f y f y f h = f + g Fortran 1 3 a b c c(1) = a(1) + b(1) c(

Fortran90/95 2. (p 74) f g h x y z f x h x = f x + g x h y = f y + g y h z = f z + g z f x f y f y f h = f + g Fortran 1 3 a b c c(1) = a(1) + b(1) c( Fortran90/95 4.1 1. n n = 5 x1,x2,x3,,x4,x5 5 average = ( x1 + x2 + x3 + x4 + x5 )/5.0 n n x (subscript) x 1 x 2 average = 1 n n x i i=1 Fortran ( ) x(1) x(2) x(n) Fortran ( ) average = sum(x(1:n))/real(n)

More information

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó 2 212 4 13 1 (4/6) : ruby 2 / 35 ( ) : gnuplot 3 / 35 ( ) 4 / 35 (summary statistics) : (mean) (median) (mode) : (range) (variance) (standard deviation) 5 / 35 (mean): x = 1 n (median): { xr+1 m, m = 2r

More information

x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n

x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n 1, R f : R R,.,, b R < b, f(x) [, b] f(x)dx,, [, b] f(x) x ( ) ( 1 ). y y f(x) f(x)dx b x 1: f(x)dx, [, b] f(x) x ( ).,,,,,., f(x)dx,,,, f(x)dx. 1.1 Riemnn,, [, b] f(x) x., x 0 < x 1 < x 2 < < x n 1

More information

mugensho.dvi

mugensho.dvi 1 1 f (t) lim t a f (t) = 0 f (t) t a 1.1 (1) lim(t 1) 2 = 0 t 1 (t 1) 2 t 1 (2) lim(t 1) 3 = 0 t 1 (t 1) 3 t 1 2 f (t), g(t) t a lim t a f (t) g(t) g(t) f (t) = o(g(t)) (t a) = 0 f (t) (t 1) 3 1.2 lim

More information

DVIOUT

DVIOUT A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)

More information

untitled

untitled I 9 MPI (II) 2012 6 14 .. MPI. 1-3 sum100.f90 4 istart=myrank*25+1 iend=(myrank+1)*25 0 1 2 3 mpi_recv 3 isum1 1 isum /tmp/120614/sum100_4.f90 program sum100_4 use mpi implicit none integer :: i,istart,iend,isum,isum1,ip

More information

1 Introduction 1 (1) (2) (3) () {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a, b] lim f n (x) f(x) (1) f(x)? (2) () f(x)? b lim a f n (x)dx = b

1 Introduction 1 (1) (2) (3) () {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a, b] lim f n (x) f(x) (1) f(x)? (2) () f(x)? b lim a f n (x)dx = b 1 Introduction 2 2.1 2.2 2.3 3 3.1 3.2 σ- 4 4.1 4.2 5 5.1 5.2 5.3 6 7 8. Fubini,,. 1 1 Introduction 1 (1) (2) (3) () {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a, b] lim f n (x) f(x) (1) f(x)?

More information

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó 2 2015 4 20 1 (4/13) : ruby 2 / 49 2 ( ) : gnuplot 3 / 49 1 1 2014 6 IIJ / 4 / 49 1 ( ) / 5 / 49 ( ) 6 / 49 (summary statistics) : (mean) (median) (mode) : (range) (variance) (standard deviation) 7 / 49

More information

Microsoft Word - DF-Salford解説09.doc

Microsoft Word - DF-Salford解説09.doc Digital Fortran 解説 2009/April 1. プログラム形態とデ - タ構成 最小自乗法プログラム (testlsm.for) m 組の実験データ (x i,y i ) に最も近似する直線式 (y=ax+b) を最小自乗法で決定する 入力データは組数 mと m 組の (x i,y i ) 値 出力データは直線式の係数 a,bとなる 入力データ m=4 (x i,y i ) X=1.50

More information

情報活用資料

情報活用資料 y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 21 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 22 L A x y A L x 23 ls -l gnuplot gnuplot> plot "sine.dat"

More information

6.1 (P (P (P (P (P (P (, P (, P.101

6.1 (P (P (P (P (P (P (, P (, P.101 (008 0 3 7 ( ( ( 00 1 (P.3 1 1.1 (P.3.................. 1 1. (P.4............... 1 (P.15.1 (P.15................. (P.18............3 (P.17......... 3.4 (P................ 4 3 (P.7 4 3.1 ( P.7...........

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

¥Ñ¥Ã¥±¡¼¥¸ Rhpc ¤Î¾õ¶·

¥Ñ¥Ã¥±¡¼¥¸ Rhpc ¤Î¾õ¶· Rhpc COM-ONE 2015 R 27 12 5 1 / 29 1 2 Rhpc 3 forign MPI 4 Windows 5 2 / 29 1 2 Rhpc 3 forign MPI 4 Windows 5 3 / 29 Rhpc, R HPC Rhpc, ( ), snow..., Rhpc worker call Rhpc lapply 4 / 29 1 2 Rhpc 3 forign

More information

格子QCD実践入門

格子QCD実践入門 -- nakamura at riise.hiroshima-u.ac.jp or nakamura at an-pan.org 2013.6.26-27 1. vs. 2. (1) 3. QCD QCD QCD 4. (2) 5. QCD 2 QCD 1981 QCD Parisi, Stamatescu, Hasenfratz, etc 2 3 (Cut-Off) = +Cut-Off a p

More information

1F90/kouhou_hf90.dvi

1F90/kouhou_hf90.dvi Fortran90 3 33 1 2 Fortran90 FORTRAN 1956 IBM IBM704 FORTRAN(FORmula TRANslation ) 1965 FORTRAN66 1978 FORTRAN77 1991 Fortran90 Fortran90 Fortran Fortran90 6 Fortran90 77 90 90 Fortran90 [ ] Fortran90

More information

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£²¡Ë

OpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£²¡Ë 2013 5 30 (schedule) (omp sections) (omp single, omp master) (barrier, critical, atomic) program pi i m p l i c i t none integer, parameter : : SP = kind ( 1. 0 ) integer, parameter : : DP = selected real

More information

統計学のポイント整理

統計学のポイント整理 .. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!

More information

第13回:交差項を含む回帰・弾力性の推定

第13回:交差項を含む回帰・弾力性の推定 13 2018 7 27 1 / 31 1. 2. 2 / 31 y i = β 0 + β X x i + β Z z i + β XZ x i z i + u i, E(u i x i, z i ) = 0, E(u i u j x i, z i ) = 0 (i j), V(u i x i, z i ) = σ 2, i = 1, 2,, n x i z i 1 3 / 31 y i = β

More information

2012 IA 8 I p.3, 2 p.19, 3 p.19, 4 p.22, 5 p.27, 6 p.27, 7 p

2012 IA 8 I p.3, 2 p.19, 3 p.19, 4 p.22, 5 p.27, 6 p.27, 7 p 2012 IA 8 I 1 10 10 29 1. [0, 1] n x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 2. 1 x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 1 0 f(x)dx 3. < b < c [, c] b [, c] 4. [, b] f(x) 1 f(x) 1 f(x) [, b] 5.

More information

6.1 (P (P (P (P (P (P (, P (, P.

6.1 (P (P (P (P (P (P (, P (, P. (011 30 7 0 ( ( 3 ( 010 1 (P.3 1 1.1 (P.4.................. 1 1. (P.4............... 1 (P.15.1 (P.16................. (P.0............3 (P.18 3.4 (P.3............... 4 3 (P.9 4 3.1 (P.30........... 4 3.

More information

(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) (

(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) ( B 4 4 4 52 4/ 9/ 3/3 6 9.. y = x 2 x x = (, ) (, ) S = 2 = 2 4 4 [, ] 4 4 4 ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, 4 4 4 4 4 k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) 2 2 + ( ) 3 2 + ( 4 4 4 4 4 4 4 4 4 ( (

More information

ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y

ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y 01 4 17 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy + r (, y) z = p + qy + r 1 y = + + 1 y = y = + 1 6 + + 1 ( = + 1 ) + 7 4 16 y y y + = O O O y = y

More information

OHP.dvi

OHP.dvi 0 7 4 0000 5.. 3. 4. 5. 0 0 00 Gauss PC 0 Gauss 3 Gauss Gauss 3 4 4 4 4 3 4 4 4 4 3 4 4 4 4 3 4 4 4 4 u [] u [3] u [4] u [4] P 0 = P 0 (),3,4 (,), (3,), (4,) 0,,,3,4 3 3 3 3 4 4 4 4 0 3 6 6 0 6 3 6 0 6

More information

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552 3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n

More information

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2 1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2

More information

I L01( Wed) : Time-stamp: Wed 07:38 JST hig e, ( ) L01 I(2017) 1 / 19

I L01( Wed) : Time-stamp: Wed 07:38 JST hig e,   ( ) L01 I(2017) 1 / 19 I L01(2017-09-20 Wed) : Time-stamp: 2017-09-20 Wed 07:38 JST hig e, http://hig3.net ( ) L01 I(2017) 1 / 19 ? 1? 2? ( ) L01 I(2017) 2 / 19 ?,,.,., 1..,. 1,2,.,.,. ( ) L01 I(2017) 3 / 19 ? I. M (3 ) II,

More information

1 1 [1] ( 2,625 [2] ( 2, ( ) /

1 1 [1] ( 2,625 [2] ( 2, ( ) / [] (,65 [] (,3 ( ) 67 84 76 7 8 6 7 65 68 7 75 73 68 7 73 7 7 59 67 68 65 75 56 6 58 /=45 /=45 6 65 63 3 4 3/=36 4/=8 66 7 68 7 7/=38 /=5 7 75 73 8 9 8/=364 9/=864 76 8 78 /=45 /=99 8 85 83 /=9 /= ( )

More information

2 1,2, , 2 ( ) (1) (2) (3) (4) Cameron and Trivedi(1998) , (1987) (1982) Agresti(2003)

2 1,2, , 2 ( ) (1) (2) (3) (4) Cameron and Trivedi(1998) , (1987) (1982) Agresti(2003) 3 1 1 1 2 1 2 1,2,3 1 0 50 3000, 2 ( ) 1 3 1 0 4 3 (1) (2) (3) (4) 1 1 1 2 3 Cameron and Trivedi(1998) 4 1974, (1987) (1982) Agresti(2003) 3 (1)-(4) AAA, AA+,A (1) (2) (3) (4) (5) (1)-(5) 1 2 5 3 5 (DI)

More information

( ) x y f(x, y) = ax

( ) x y f(x, y) = ax 013 4 16 5 54 (03-5465-7040) nkiyono@mail.ecc.u-okyo.ac.jp hp://lecure.ecc.u-okyo.ac.jp/~nkiyono/inde.hml 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy

More information

演習1

演習1 神戸市立工業高等専門学校電気工学科 / 電子工学科専門科目 数値解析 2019.5.10 演習 1 山浦剛 (tyamaura@riken.jp) 講義資料ページ http://r-ccs-climate.riken.jp/members/yamaura/numerical_analysis.html Fortran とは? Fortran(= FORmula TRANslation ) は 1950

More information

Fgure : (a) precse but naccurate data. (b) accurate but mprecse data. [] Fg..(p.) Fgure : Accuracy vs Precson []p.0-0 () 05. m 0.35 m 05. ± 0.35m 05.

Fgure : (a) precse but naccurate data. (b) accurate but mprecse data. [] Fg..(p.) Fgure : Accuracy vs Precson []p.0-0 () 05. m 0.35 m 05. ± 0.35m 05. 9 3 Error Analyss [] Danel C. Harrs, Quanttatve Chemcal Analyss, Chap.3-5. th Ed. 003. [] J. R. Taylor (, 000. An Introducton to Error Analyss, nd Ed. 997 Unv. Sc. Books) [3] 00 ( [] 973 Posson [5] 99

More information

Microsoft Word - 信号処理3.doc

Microsoft Word - 信号処理3.doc Junji OHTSUBO 2012 FFT FFT SN sin cos x v ψ(x,t) = f (x vt) (1.1) t=0 (1.1) ψ(x,t) = A 0 cos{k(x vt) + φ} = A 0 cos(kx ωt + φ) (1.2) A 0 v=ω/k φ ω k 1.3 (1.2) (1.2) (1.2) (1.1) 1.1 c c = a + ib, a = Re[c],

More information

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory 10.3 Fubini 1 Introduction [1],, [2],, [3],, [4],, [5],, [6],, [7],, [8],, [1, 2, 3] 1980

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory 10.3 Fubini 1 Introduction [1],, [2],, [3],, [4],, [5],, [6],, [7],, [8],, [1, 2, 3] 1980 % 100% 1 Introduction 2 (100%) 2.1 2.2 2.3 3 (100%) 3.1 3.2 σ- 4 (100%) 4.1 4.2 5 (100%) 5.1 5.2 5.3 6 (100%) 7 (40%) 8 Fubini (90%) 2006.11.20 1 8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory

More information

main.dvi

main.dvi 3 4 2 3 4 2 3 ( ) ( ) 1 1.1 R n R n n Euclid R n R n f =(f 1 ;f 2 ;:::;f n ) T : f(x) =0 (1) x = (x 1 ;x 2 ;:::;x n ) T 2 R n 1 \T " f i (1 i n) R n R (1) f i (x) =0 (1 i n) n 2 n x =cosx f(x) :=x 0 cos

More information

D0050.PDF

D0050.PDF Excel VBA 6 3 3 1 Excel BLOCKGAME.xls Excel 1 OK 2 StepA D B1 B4 C1 C2 StepA StepA Excel Workbook Open StepD BLOCKGAME.xls VBEditor ThisWorkbook 3 1 1 2 2 3 5 UserForm1 4 6 UsorForm2 StepB 3 StepC StepD

More information

70の法則

70の法則 70 70 1 / 27 70 1 2 3 4 5 6 2 / 27 70 70 70 X r % = 70 2 r r r 10 72 70 72 70 : 1, 2, 5, 7, 10, 14, 35, 70 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 3 / 27 r = 10 70 r = 10 70 1 : X, X 10 = ( X + X

More information

Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1) (2) ( ) BASIC BAS

Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1) (2) ( ) BASIC BAS Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1 (2 ( BASIC BASIC download TUTORIAL.PDF http://hp.vector.co.jp/authors/va008683/

More information

C言語によるアルゴリズムとデータ構造

C言語によるアルゴリズムとデータ構造 Algorithms and Data Structures in C 4 algorithm List - /* */ #include List - int main(void) { int a, b, c; int max; /* */ Ÿ 3Ÿ 2Ÿ 3 printf(""); printf(""); printf(""); scanf("%d", &a); scanf("%d",

More information

Acrobat Distiller, Job 128

Acrobat Distiller, Job 128 (2 ) 2 < > ( ) f x (x, y) 2x 3+y f y (x, y) x 2y +2 f(3, 2) f x (3, 2) 5 f y (3, 2) L y 2 z 5x 5 ` x 3 z y 2 2 2 < > (2 ) f(, 2) 7 f x (x, y) 2x y f x (, 2),f y (x, y) x +4y,f y (, 2) 7 z (x ) + 7(y 2)

More information

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0,

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0, .1.1 Y K L Y = K 1 3 L 3 L K K (K + ) 1 1 3 L 3 K 3 L 3 K 0 (K + K) 1 3 L 3 K 1 3 L 3 lim K 0 K = L (K + K) 1 3 K 1 3 3 lim K 0 K = 1 3 K 3 L 3 z = f(x, y) x y z x-y-z.1 z = e x +xy y 3 x-y ( ) z 0 f(x,

More information

i

i i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,

More information

B 90 Canvas.Pen.Width := PenWidth; NewData; (* FormCreate (*********************** ******************* procedure TFormSorting.DrawOne(No : TDat

B 90 Canvas.Pen.Width := PenWidth; NewData; (* FormCreate (*********************** ******************* procedure TFormSorting.DrawOne(No : TDat B 89 14 14.1 14.1.1 SortingU SortingP 14.1.2 Form Name FormSorting Caption Position podesktopcenter 14.1.3 14.1.4 const NoMax = 400; DataMax = 600; PenWidth = 2; type TDataNo = 0..NoMax; TData = array

More information

sim98-8.dvi

sim98-8.dvi 8 12 12.1 12.2 @u @t = @2 u (1) @x 2 u(x; 0) = (x) u(0;t)=u(1;t)=0fort 0 1x, 1t N1x =1 x j = j1x, t n = n1t u(x j ;t n ) Uj n U n+1 j 1t 0 U n j =1t=(1x) 2 = U n j+1 0 2U n j + U n j01 (1x) 2 (2) U n+1

More information

N88 BASIC 0.3 C: My Documents 0.6: 0.3: (R) (G) : enterreturn : (F) BA- SIC.bas 0.8: (V) 0.9: 0.5:

N88 BASIC 0.3 C: My Documents 0.6: 0.3: (R) (G) : enterreturn : (F) BA- SIC.bas 0.8: (V) 0.9: 0.5: BASIC 20 4 10 0 N88 Basic 1 0.0 N88 Basic..................................... 1 0.1............................................... 3 1 4 2 5 3 6 4 7 5 10 6 13 7 14 0 N88 Basic 0.0 N88 Basic 0.1: N88Basic

More information

( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1

( )/2   hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1 ( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S

More information

body.dvi

body.dvi ..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................

More information

i 18 2H 2 + O 2 2H 2 + ( ) 3K

i 18 2H 2 + O 2 2H 2 + ( ) 3K i 18 2H 2 + O 2 2H 2 + ( ) 3K ii 1 1 1.1.................................. 1 1.2........................................ 3 1.3......................................... 3 1.4....................................

More information

[ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx A p.2/29

[ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx A p.2/29 A p./29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx A p.2/29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx [ ] F(x) f(x) C F(x) + C f(x) A p.2/29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx [ ] F(x) f(x) C F(x)

More information

CALCULUS II (Hiroshi SUZUKI ) f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b)

CALCULUS II (Hiroshi SUZUKI ) f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b) CALCULUS II (Hiroshi SUZUKI ) 16 1 1 1.1 1.1 f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b) lim f(x, y) = lim f(x, y) = lim f(x, y) = c. x a, y b

More information

ex01.dvi

ex01.dvi ,. 0. 0.0. C () /******************************* * $Id: ex_0_0.c,v.2 2006-04-0 3:37:00+09 naito Exp $ * * 0. 0.0 *******************************/ #include int main(int argc, char **argv) double

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information